Walking, although a largely automatic process, is controlled by the cortex and the spinal cord with corrective reflexes modulated through integration of neural signals from central and peripheral inputs at supraspinal level throughout the gait cycle. In this study we used an additional cognitive task to interfere with the automatic processing during walking in order to explore the neural mechanisms involved in healthy young adults. Participants were asked to walk on a treadmill at two speeds, both with and without additional cognitive load. We evaluated the impact of speed and cognitive load by analyzing activity of the prefrontal cortex (PFC) using functional Near-Infrared Spectroscopy (fNIRS) alongside spinal cord reflex activity measured by soleus H-reflex amplitude and gait changes obtained by using an inertial measuring unit. Repeated measures ANOVA revealed that fNIRS Oxy-Hb concentrations significantly increased in the PFC with dual task (walking while performing a cognitive task) compared to a single task (walking only; p < 0.05). PFC activity was unaffected by increases of walking speed. H-reflex amplitude and gait variables did not change in response to either dual task or increases in walking speed. When walking under additional cognitive load participants adapted by using greater activity in the PFC, but this adaptation did not detrimentally affect H-reflex amplitude or gait variables. Our findings suggest that in a healthy young population central mechanisms (PFC) are activated in response to cognitive loads but that H-reflex activity and gait performance can successfully be maintained. This study provides insights into the mechanisms behind healthy individuals safely performing dual task walking.